00:01
Okay, we're given the polar equation r equals for cosine of 3 theta.
00:06
We are going to sketch it and find the area.
00:09
So normally with a sketch, we look at important values that result in inside the cosine being like 0, pi over 2, pi.
00:20
However, that's going to, you know, we're going to have to use a lot of pies over 6es in order to when we multiply it by 3.
00:27
Or, you know, we'll have to kind of be thinking a lot about our fractions.
00:33
So because of the 3 theta, i'm going to go ahead and show you how to graph this a little bit differently.
00:42
So with the 3 inside, i know that there are three cosines between 0 and 2 pi.
00:48
So if there's three of these, and i visually see it, i can break these down into very symmetric pieces.
00:56
So i can almost count.
00:57
How many of, you know, for every period i can consider the downward swing and then the upward swing.
01:03
So there's like one, two, three, four, five, six.
01:07
So halfway would be at the three of those.
01:11
And so i can put pie there.
01:12
And then i can again break these down into parts.
01:15
Instead of maybe doing full swings, i can look at those half and again break it in half.
01:21
So i'm using a nice, you know, picture to be able to think about where.
01:27
Important places are.
01:29
So i'm in quadrant one from zero to pi over two, but there's going to be some negative r values.
01:36
And so instead, they'll be flipped to the other side and be in quadrant three.
01:42
So also, i know a third of the way between zero and pi over two...